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mhn 0.1.0

Initial release.

Distribution functions

• dmhn(), pmhn(), qmhn(), and rmhn() provide density, distribution, quantile, and random generation for the Modified Half-Normal (MHN) distribution of Sun, Kong & Pal (2023).
• All four functions are vectorised over both the evaluation argument and the parameters alpha, beta, gamma, following standard R recycling rules.
• A ParamCache reuses the Fox–Wright Psi normalising constant across consecutive elements that share an (alpha, beta, gamma) triple, so grouped inputs are evaluated significantly faster than calling the functions inside an R loop.

Random generation

• rmhn(..., method = "auto") (default) routes each parameter triple to the cheapest provably-correct sampler: closed-form shortcuts for the special cases, Sun et al. (2023, Algorithms 1 and 3) where they win, and the Gao & Wang (2025) Relaxed Transformed Density Rejection (RTDR) sampler elsewhere.
• method = "rtdr" forces RTDR with its uniform 1/e acceptance bound.
• method = "sun" forces Sun Algorithm 1 (gamma > 0, alpha > 1) or Algorithm 3 (gamma <= 0); Sun Algorithm 2 is intentionally not implemented and an unsupported combination triggers a clear error.

CDF and quantile

• pmhn() uses the Sun et al. (2023, Lemma 1b) series in log space, truncated at the Sun et al. (2023, Supplementary Lemma 10(d)) constructive bound K = max(K1, K2); the truncation residual is bounded by the user’s tolerance divided by Psi.
• For gamma < 0 the series uses sign-separated log-sum-exp + log- diff-exp accumulation and a runtime cancellation guard derived from the double-precision precision floor: when the relative cancellation loss would exceed the user’s tolerance, pmhn() falls back to a peak-normalised Boost.Math quadrature (Gauss-Kronrod for alpha >= 1, tanh-sinh for alpha < 1) of the unnormalised density.
• qmhn() inverts pmhn() via boost::math::tools::toms748_solve on the bracket [sqrt(eps), E(X) + 8 sqrt(Var(X))], doubling the upper end as needed.

Summary statistics

• mhn_mean(), mhn_var(), mhn_skewness(), mhn_kurtosis(), and mhn_mode() evaluate the closed-form / recurrence-based expressions from Sun et al. (2023, Lemmas 2 and 3).

Tests and documentation

• testthat suite with > 1,700 expectations covering goodness-of-fit (Kolmogorov-Smirnov), special-case identities, vectorised recycling, NA / NaN propagation, and the Sun / Gao & Wang acceptance bounds.
• vignette("introduction", package = "mhn") walks through every exported function with runnable examples.
• vignette("theory", package = "mhn") is the theoretical companion: it covers the MHN family and its special cases, the Fox–Wright Psi normalising constant, Algorithms 1 and 3 of Sun et al. (2023), the four-region Gao & Wang RTDR construction, and the rmhn(method = "auto") decision tree.
• citation("mhn") returns three bibentry objects: the package, the Sun et al. (2023) paper, and the Gao & Wang (2025) paper.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.